The tutorial and the code are written by User:sphinkie.
You can also react to this article in the forum
Table of contents
Thanks to Snowblind for the ManualSphereMeshes and its "shape to mesh" algorithm.
Thanks to Richard J. Bono for the geodesic algorithm (GNU licence) and the
In this article, I will present a way to generate various geometric shapes. This article gives information about the library, the concept, and how to use it.
The UV mapping applied on all shapes is a spherical mapping. The library can be upgraded for bugfix, optimization and adding new shapes.
All the sources can be found at the end of the article.
The API is quite simple, and you can built it using the utility doxygen (as the source files are doxygen compatible).
When you create the object, you give the parameters needed: usually radius, and some others. It depend of the kind of shape you are creating. Then you call the createMesh method, giving the name of the mesh. You will use the same name when creating your Ogre entity.
- Example 1: creating a cube with a halfside of 100 units:
#include "Mesh_Cube.h" ... Mesh_Cube M(100); M.createMesh("myMesh"); mEntity = mSceneMgr->createEntity(mName, "myMesh"); mNode->attachObject(mEntity);
: A textured cube
- Example 2: creating a geosphere with a radius of 800 units:
#include "Mesh_geosphere.h" ... Mesh_Geosphere M(800); // radius 800 - default frequency - default class 1 // Mesh_Geosphere M(800, 4, true); // radius 800 - frequency 4 - class 2 M.createMesh("myMesh"); ... // extra functions available for geodesic shapes: M.dumpData(); // write data inthe log file M.createDXF("geosphere.dxf"); // create a DXF file M.createDXFwireframe("geosphere_WF.dxf"); // create a DXF file ... mEntity = mSceneMgr->createEntity(mName, "myMesh"); mNode->attachObject(mEntity);
For geodesic shapes, you have some more functions in the API that allow you to dump geometrical data in the log file, and to create a DXF file, so you can preview the shape in your favorite 3D modeler (ie: blender3D).
: A textured geosphere
- Example 3: creating a sphere with a radius of 800 units.:
#include "Mesh_sphere.h" ... Mesh_Sphere M(800); M.createMesh("myMesh"); mEntity = mSceneMgr->createEntity(mName, "myMesh"); mNode->attachObject(mEntity);
: A wireframe sphere
The library is based on 2 generic classes : GeometricMesh and Geodesic.
GeometricMesh allows you to create geometric meshes, when given a certain number of vertices and triangles.
The GeometricMesh class itself cannot create any meshes. This class should be derived from, with a function fillMesh() defining the positions of all vertices.
Existing derived class are: Mesh_Cube, Mesh_Icosa, Mesh_Sphere.
New classes can be easily added (cylinder, etc).
- In a Cube, or an Icosahedron, there is a small number of vertices (around 10 or 20), so the list of vertices can be manually defined.
- In a Sphere, a simple function can be use to define all the vertex positions (thanks to the 'snowblind' equation). A function also allows you to create spheres with a parameterizable number of vertices.
- But to create a geosphere, a more complex function is needed, and we will need another class (Geodesic) to generate the list of vertices for these shapes.
Geodesic shapes a large family of shapes, usually used in architecture for domes, honeycomb, etc. For us, we are only interrested a the subfamily based on assembly of triangles. (you can also have assembly of hexagons or pentagons).
The Geodesic class itself gives you no shape: it has to derived into classes that define the equation of the points of the shapes.
Existing class are Mesh_geosphere and Mesh_geoellipse.
New classes can be added, but it is not so easy...
Geosphere is a good shape for planets, as is has less texture distortion at the pole (like the usual sphere has).
Geoellipse allow you to create Zeppelin shapes, flying saucers, eggs...
Class 1 geosphere
Class 2 geosphere
Class 2 geoellipse
- The main reference used in the creation of the geodesic code was "Geodesic Math & How to Use It" by Hugh Kenner, 1976, University of California Press. ISBN 0-520-02924-0
- Richard Hawkins digital archive
- Geodesic Dome Design
- The Math Forum
- Open Scene Graph Tutorials
- L'icosaedre (french)
- And Of course, Wikipedia
This is 1.1 version. All source files are in this zip file:
The API can be found here Dead Link
To compile you may need these lines in your macros.h.
#define DEBUG_LOG(X) Ogre::LogManager::getSingleton().logMessage(X) #define TRACE(X) Ogre::LogManager::getSingleton().logMessage(X)
Or these lines, if you want to disable the debug log.
#define DEBUG_LOG(X) #define TRACE(X) Ogre::LogManager::getSingleton().logMessage(X)
- odd frequency with a class 2 geosphere give strange results.
For the moment, if you want to add/modify the source code, please send me your files and I will update the zip file, or use the Discussion tab of this page.
These functionnalities are not implemented yet in the library:
- Une the new MeshFactory, available in the 'Dagon' version of Ogre3D.
- Optimization of the vertex number. When the vertice list is defined by a function, it usually creates several vertices for the same point. ie: if a point belongs to 5 triangles, 5 vertices are usually generated for this point.
- New shape : A Cylinder
- New shape : A Torus
- In the geosphere, there are 2 points with X=0 and Z=0 (the poles). This makes the calculation of U coordinate difficult. The solution is maybe to pitch a bit the shape before transforming it into a mesh.
THE WORK (AS DEFINED BELOW) IS PROVIDED UNDER THE TERMS OF THIS CREATIVE COMMONS PUBLIC LICENSE ("CCPL" OR "LICENSE"). THE WORK IS PROTECTED BY COPYRIGHT AND/OR OTHER APPLICABLE LAW. ANY USE OF THE WORK OTHER THAN AS AUTHORIZED UNDER THIS LICENSE OR COPYRIGHT LAW IS PROHIBITED.
BY EXERCISING ANY RIGHTS TO THE WORK PROVIDED HERE, YOU ACCEPT AND AGREE TO BE BOUND BY THE TERMS OF THIS LICENSE. THE LICENSOR GRANTS YOU THE RIGHTS CONTAINED HERE IN CONSIDERATION OF YOUR ACCEPTANCE OF SUCH TERMS AND CONDITIONS.
- "Collective Work" means a work, such as a periodical issue, anthology or encyclopedia, in which the Work in its entirety in unmodified form, along with a number of other contributions, constituting separate and independent works in themselves, are assembled into a collective whole. A work that constitutes a Collective Work will not be considered a Derivative Work (as defined below) for the purposes of this License.
- "Derivative Work" means a work based upon the Work or upon the Work and other pre-existing works, such as a translation, musical arrangement, dramatization, fictionalization, motion picture version, sound recording, art reproduction, abridgment, condensation, or any other form in which the Work may be recast, transformed, or adapted, except that a work that constitutes a Collective Work will not be considered a Derivative Work for the purpose of this License. For the avoidance of doubt, where the Work is a musical composition or sound recording, the synchronization of the Work in timed-relation with a moving image ("synching") will be considered a Derivative Work for the purpose of this License.
- "Licensor" means the individual or entity that offers the Work under the terms of this License.
- "Original Author" means the individual or entity who created the Work.
- "Work" means the copyrightable work of authorship offered under the terms of this License.
- "You" means an individual or entity exercising rights under this License who has not previously violated the terms of this License with respect to the Work, or who has received express permission from the Licensor to exercise rights under this License despite a previous violation.
- "License Elements" means the following high-level license attributes as selected by Licensor and indicated in the title of this License: Attribution, ShareAlike.
Nothing in this license is intended to reduce, limit, or restrict any rights arising from fair use, first sale or other limitations on the exclusive rights of the copyright owner under copyright law or other applicable laws.
Subject to the terms and conditions of this License, Licensor hereby grants You a worldwide, royalty-free, non-exclusive, perpetual (for the duration of the applicable copyright) license to exercise the rights in the Work as stated below:
- to reproduce the Work, to incorporate the Work into one or more Collective Works, and to reproduce the Work as incorporated in the Collective Works;
- to create and reproduce Derivative Works;
- to distribute copies or phonorecords of, display publicly, perform publicly, and perform publicly by means of a digital audio transmission the Work including as incorporated in Collective Works;
- to distribute copies or phonorecords of, display publicly, perform publicly, and perform publicly by means of a digital audio transmission Derivative Works.
- For the avoidance of doubt, where the work is a musical composition:
- Performance Royalties Under Blanket Licenses. Licensor waives the exclusive right to collect, whether individually or via a performance rights society (e.g. ASCAP, BMI, SESAC), royalties for the public performance or public digital performance (e.g. webcast) of the Work.
- Mechanical Rights and Statutory Royalties. Licensor waives the exclusive right to collect, whether individually or via a music rights society or designated agent (e.g. Harry Fox Agency), royalties for any phonorecord You create from the Work ("cover version") and distribute, subject to the compulsory license created by 17 USC Section 115 of the US Copyright Act (or the equivalent in other jurisdictions).
- Webcasting Rights and Statutory Royalties. For the avoidance of doubt, where the Work is a sound recording, Licensor waives the exclusive right to collect, whether individually or via a performance-rights society (e.g. SoundExchange), royalties for the public digital performance (e.g. webcast) of the Work, subject to the compulsory license created by 17 USC Section 114 of the US Copyright Act (or the equivalent in other jurisdictions).
The above rights may be exercised in all media and formats whether now known or hereafter devised. The above rights include the right to make such modifications as are technically necessary to exercise the rights in other media and formats. All rights not expressly granted by Licensor are hereby reserved.
The license granted in Section 3 above is expressly made subject to and limited by the following restrictions:
- You may distribute, publicly display, publicly perform, or publicly digitally perform the Work only under the terms of this License, and You must include a copy of, or the Uniform Resource Identifier for, this License with every copy or phonorecord of the Work You distribute, publicly display, publicly perform, or publicly digitally perform. You may not offer or impose any terms on the Work that alter or restrict the terms of this License or the recipients' exercise of the rights granted hereunder. You may not sublicense the Work. You must keep intact all notices that refer to this License and to the disclaimer of warranties. You may not distribute, publicly display, publicly perform, or publicly digitally perform the Work with any technological measures that control access or use of the Work in a manner inconsistent with the terms of this License Agreement. The above applies to the Work as incorporated in a Collective Work, but this does not require the Collective Work apart from the Work itself to be made subject to the terms of this License. If You create a Collective Work, upon notice from any Licensor You must, to the extent practicable, remove from the Collective Work any credit as required by clause 4(c), as requested. If You create a Derivative Work, upon notice from any Licensor You must, to the extent practicable, remove from the Derivative Work any credit as required by clause 4(c), as requested.
- You may distribute, publicly display, publicly perform, or publicly digitally perform a Derivative Work only under the terms of this License, a later version of this License with the same License Elements as this License, or a Creative Commons iCommons license that contains the same License Elements as this License (e.g. Attribution-ShareAlike 2.5 Japan). You must include a copy of, or the Uniform Resource Identifier for, this License or other license specified in the previous sentence with every copy or phonorecord of each Derivative Work You distribute, publicly display, publicly perform, or publicly digitally perform. You may not offer or impose any terms on the Derivative Works that alter or restrict the terms of this License or the recipients' exercise of the rights granted hereunder, and You must keep intact all notices that refer to this License and to the disclaimer of warranties. You may not distribute, publicly display, publicly perform, or publicly digitally perform the Derivative Work with any technological measures that control access or use of the Work in a manner inconsistent with the terms of this License Agreement. The above applies to the Derivative Work as incorporated in a Collective Work, but this does not require the Collective Work apart from the Derivative Work itself to be made subject to the terms of this License.
- If you distribute, publicly display, publicly perform, or publicly digitally perform the Work or any Derivative Works or Collective Works, You must keep intact all copyright notices for the Work and provide, reasonable to the medium or means You are utilizing: (i) the name of the Original Author (or pseudonym, if applicable) if supplied, and/or (ii) if the Original Author and/or Licensor designate another party or parties (e.g. a sponsor institute, publishing entity, journal) for attribution in Licensor's copyright notice, terms of service or by other reasonable means, the name of such party or parties; the title of the Work if supplied; to the extent reasonably practicable, the Uniform Resource Identifier, if any, that Licensor specifies to be associated with the Work, unless such URI does not refer to the copyright notice or licensing information for the Work; and in the case of a Derivative Work, a credit identifying the use of the Work in the Derivative Work (e.g., "French translation of the Work by Original Author," or "Screenplay based on original Work by Original Author"). Such credit may be implemented in any reasonable manner; provided, however, that in the case of a Derivative Work or Collective Work, at a minimum such credit will appear where any other comparable authorship credit appears and in a manner at least as prominent as such other comparable authorship credit.
UNLESS OTHERWISE AGREED TO BY THE PARTIES IN WRITING, LICENSOR OFFERS THE WORK AS-IS AND MAKES NO REPRESENTATIONS OR WARRANTIES OF ANY KIND CONCERNING THE MATERIALS, EXPRESS, IMPLIED, STATUTORY OR OTHERWISE, INCLUDING, WITHOUT LIMITATION, WARRANTIES OF TITLE, MERCHANTIBILITY, FITNESS FOR A PARTICULAR PURPOSE, NONINFRINGEMENT, OR THE ABSENCE OF LATENT OR OTHER DEFECTS, ACCURACY, OR THE PRESENCE OF ABSENCE OF ERRORS, WHETHER OR NOT DISCOVERABLE. SOME JURISDICTIONS DO NOT ALLOW THE EXCLUSION OF IMPLIED WARRANTIES, SO SUCH EXCLUSION MAY NOT APPLY TO YOU.
EXCEPT TO THE EXTENT REQUIRED BY APPLICABLE LAW, IN NO EVENT WILL LICENSOR BE LIABLE TO YOU ON ANY LEGAL THEORY FOR ANY SPECIAL, INCIDENTAL, CONSEQUENTIAL, PUNITIVE OR EXEMPLARY DAMAGES ARISING OUT OF THIS LICENSE OR THE USE OF THE WORK, EVEN IF LICENSOR HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.
- This License and the rights granted hereunder will terminate automatically upon any breach by You of the terms of this License. Individuals or entities who have received Derivative Works or Collective Works from You under this License, however, will not have their licenses terminated provided such individuals or entities remain in full compliance with those licenses. Sections 1, 2, 5, 6, 7, and 8 will survive any termination of this License.
- Subject to the above terms and conditions, the license granted here is perpetual (for the duration of the applicable copyright in the Work). Notwithstanding the above, Licensor reserves the right to release the Work under different license terms or to stop distributing the Work at any time; provided, however that any such election will not serve to withdraw this License (or any other license that has been, or is required to be, granted under the terms of this License), and this License will continue in full force and effect unless terminated as stated above.
- Each time You distribute or publicly digitally perform the Work or a Collective Work, the Licensor offers to the recipient a license to the Work on the same terms and conditions as the license granted to You under this License.
- Each time You distribute or publicly digitally perform a Derivative Work, Licensor offers to the recipient a license to the original Work on the same terms and conditions as the license granted to You under this License.
- If any provision of this License is invalid or unenforceable under applicable law, it shall not affect the validity or enforceability of the remainder of the terms of this License, and without further action by the parties to this agreement, such provision shall be reformed to the minimum extent necessary to make such provision valid and enforceable.
- No term or provision of this License shall be deemed waived and no breach consented to unless such waiver or consent shall be in writing and signed by the party to be charged with such waiver or consent.
- This License constitutes the entire agreement between the parties with respect to the Work licensed here. There are no understandings, agreements or representations with respect to the Work not specified here. Licensor shall not be bound by any additional provisions that may appear in any communication from You. This License may not be modified without the mutual written agreement of the Licensor and You.